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Sep 20, 2013
09/13

by
Thomas Chen; Juerg Froehlich; Johannes Walcher

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We study the classical decay of unstable scalar solitons in noncommutative field theory in 2+1 dimensions. This can, but does not have to, be viewed as a toy model for the decay of D-branes in string theory. In the limit that the noncommutativity parameter \theta is infinite, the gradient term is absent, there are no propagating modes and the soliton does not decay at all. If \theta is large, but finite, the rotationally symmetric decay channel can be described as a highly excited nonlinear...

Source: http://arxiv.org/abs/hep-th/0301119v2

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61

Sep 18, 2013
09/13

by
Kentaro Hori; Johannes Walcher

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We construct and classify categories of D-branes in orientifolds based on Landau-Ginzburg models and their orbifolds. Consistency of the worldsheet parity action on the matrix factorizations plays the key role. This provides all the requisite data for an orientifold construction after embedding in string theory. One of our main results is a computation of topological field theory correlators on unoriented worldsheets, generalizing the formulas of Vafa and Kapustin-Li for oriented worldsheets,...

Source: http://arxiv.org/abs/hep-th/0606179v1

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Jun 28, 2018
06/18

by
Marc-Antoine Fiset; Johannes Walcher

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The SCHOK bound states that the number of marginal deformations of certain two-dimensional conformal field theories is bounded linearly from above by the number of relevant operators. In conformal field theories defined via sigma models into Calabi-Yau manifolds, relevant operators can be estimated, in the point-particle approximation, by the low-lying spectrum of the scalar Laplacian on the manifold. In the strict large volume limit, the standard asymptotic expansion of Weyl and...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1506.08407

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53

Sep 18, 2013
09/13

by
Johannes Walcher

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Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open Gromov-Witten invariants, satisfies a certain extension of the Picard-Fuchs differential equation governing periods of the mirror quintic. We verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space....

Source: http://arxiv.org/abs/hep-th/0605162v2

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Sep 23, 2013
09/13

by
Johannes Walcher

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We study normal functions capturing D-brane superpotentials on several one- and two-parameter Calabi-Yau hypersurfaces and complete intersections in weighted projective space. We calculate in the B-model and interpret the results using mirror symmetry in the large volume regime, albeit without identifying the precise A-model geometry in all cases. We identify new classes of extensions of Picard-Fuchs equations, as well as a novel type of topology changing phase transition involving quantum...

Source: http://arxiv.org/abs/0904.4905v1

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Sep 21, 2013
09/13

by
David R. Morrison; Johannes Walcher

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We explain the B-model origin of extended Picard-Fuchs equations satisfied by the D-brane superpotential on compact Calabi-Yau threefolds. Via the Abel-Jacobi map, the domainwall tension is identified with a Poincare normal function--a transversal holomorphic section of the Griffiths intermediate Jacobian. Within this formalism, we derive the extended Picard-Fuchs equation associated with the mirror of the real quintic.

Source: http://arxiv.org/abs/0709.4028v1

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Sep 21, 2013
09/13

by
Sebastian Franco; Yang-Hui He; Christopher Herzog; Johannes Walcher

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We investigate the general features of renormalization group flows near superconformal fixed points of four dimensional N=1 supersymmetric gauge theories with gravity duals. The gauge theories we study arise as the world-volume theory on a set of D-branes at a Calabi-Yau singularity where a del Pezzo surface shrinks to zero size. Based mainly on field theory analysis, we find evidence that such flows are often chaotic and contain exotic features such as duality walls. For a gauge theory where...

Source: http://arxiv.org/abs/hep-th/0402120v2

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3.0

Jun 30, 2018
06/18

by
Daniel Krefl; Johannes Walcher

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This is the 13th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. It discusses the relation between the instanton partition functions and the partition function of the topological string from the perspective of the B-model. The instanton partition functions provide solutions to the holomorphic anomaly equations characterising the partition functions of the topological string.

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1412.7133

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3.0

Jun 30, 2018
06/18

by
Albert Schwarz; Vadim Vologodsky; Johannes Walcher

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We say that a formal power series $\sum a_n z^n$ with rational coefficients is a 2-function if the numerator of the fraction $a_{n/p}-p^2 a_n$ is divisible by $p^2$ for every prime number $p$. One can prove that 2-functions with rational coefficients appear as building block of BPS generating functions in topological string theory. Using the Frobenius map we define 2-functions with coefficients in algebraic number fields. We establish two results pertaining to these functions. First, we show...

Topics: High Energy Physics - Theory, Algebraic Geometry, Number Theory, Mathematics

Source: http://arxiv.org/abs/1702.07135

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Sep 21, 2013
09/13

by
Shmuel Elitzur; Yaron Oz; Eliezer Rabinovici; Johannes Walcher

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We consider the topological sigma-model on Riemann surfaces with genus g and h holes, and target space CP1. We calculate the correlation functions of bulk and boundary operators, and study the symmetries of the model and its most general deformation. We study the open/closed topological field theory (TFT) correspondence by summing up the boundaries. We argue that this summation can be understood as a renormalization of the closed TFT. We couple the model to topological gravity and derive...

Source: http://arxiv.org/abs/1106.2967v2

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Sep 17, 2013
09/13

by
Alex Buchel; Johannes Walcher

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This is a note on the coupled supergravity-tachyon matter system, which has been earlier proposed as a candidate for the effective space-time description of S-branes. In particular, we study an ansatz with the maximal ISO(p+1)xSO(8-p,1) symmetry, for general brane dimensionality p and homogeneous brane distribution in transverse space \rho_\perp. A simple application of singularity theorems shows that (for p \le 7) the most general solution with these symmetries is always singular. (This...

Source: http://arxiv.org/abs/hep-th/0305055v3

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Sep 20, 2013
09/13

by
Kentaro Hori; Johannes Walcher

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We study marginal deformations of B-type D-branes in Landau-Ginzburg orbifolds. The general setup of matrix factorizations allows for exact computations of F-term equations in the low-energy effective theory which are much simpler than in a corresponding geometric description. We present a number of obstructed and unobstructed examples in detail, including one in which a closed string modulus is obstructed by the presence of D-branes. In a certain example, we find a non-trivial global structure...

Source: http://arxiv.org/abs/hep-th/0404196v2

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Sep 18, 2013
09/13

by
Johannes Walcher

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Open topological string amplitudes on compact Calabi-Yau threefolds are shown to satisfy an extension of the holomorphic anomaly equation of Bershadsky, Cecotti, Ooguri and Vafa. The total topological charge of the D-brane configuration must vanish in order to satisfy tadpole cancellation. The boundary state of such D-branes is holomorphically captured by a Hodge theoretic normal function. Its Griffiths' infinitesimal invariant is the analogue of the closed string Yukawa coupling and plays the...

Source: http://arxiv.org/abs/0705.4098v4

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Sep 21, 2013
09/13

by
Daniel Krefl; Johannes Walcher

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We study the topological string on local P2 with O-plane and D-brane at its real locus, using three complementary techniques. In the A-model, we refine localization on the moduli space of maps with respect to the torus action preserved by the anti-holomorphic involution. This leads to a computation of open and unoriented Gromov-Witten invariants that can be applied to any toric Calabi-Yau with involution. We then show that the full topological string amplitudes can be reproduced within the...

Source: http://arxiv.org/abs/0902.0616v1

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Sep 20, 2013
09/13

by
Radu Roiban; Radu Tatar; Johannes Walcher

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The proper inclusion of flavor in the Dijkgraaf-Vafa proposal for the solution of N=1 gauge theories through matrix models has been subject of debate in the recent literature. We here reexamine this issue by geometrically engineering fundamental matter with type IIB branes wrapped on non-compact cycles in the resolved geometry, and following them through the geometric transition. Our approach treats massive and massless flavor fields on equal footing, including the mesons. We also study the...

Source: http://arxiv.org/abs/hep-th/0301217v1

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Sep 17, 2013
09/13

by
Alex Buchel; Peter Langfelder; Johannes Walcher

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Time-dependent solutions of supergravity and string theory are studied. The examples are obtained from de Sitter deformation of gauge/gravity dualities, analytical continuation of static solutions, and ``exactly solvable'' worldsheet models. Among other things, it is shown that turning on a Hubble parameter in the background of a confining gauge theory in four dimensions can restore chiral symmetry. Some of the solutions obtained from analytical continuation have the interpretation of a...

Source: http://arxiv.org/abs/hep-th/0207214v2

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Sep 23, 2013
09/13

by
Ilka Brunner; Manfred Herbst; Wolfgang Lerche; Johannes Walcher

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We revisit open string mirror symmetry for the elliptic curve, using matrix factorizations for describing D-branes on the B-model side. We show how flat coordinates can be intrinsically defined in the Landau-Ginzburg model, and derive the A-model partition function counting disk instantons that stretch between three D-branes. In mathematical terms, this amounts to computing the simplest Fukaya product m_2 from the LG mirror theory. In physics terms, this gives a systematic method for...

Source: http://arxiv.org/abs/hep-th/0408243v1

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Sep 17, 2013
09/13

by
Hans Jockers; Peter Mayr; Johannes Walcher

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We show that certain superpotential and Kahler potential couplings of N=1 supersymmetric compactifications with branes or bundles can be computed from Hodge theory and mirror symmetry. This applies to F-theory on a Calabi-Yau four-fold and three-fold compactifications of type II and heterotic strings with branes. The heterotic case includes a class of bundles on elliptic manifolds constructed by Friedmann, Morgan and Witten. Mirror symmetry of the four-fold computes non-perturbative corrections...

Source: http://arxiv.org/abs/0912.3265v2

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Sep 21, 2013
09/13

by
Johannes Walcher

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We study the topological string on compact Calabi-Yau threefolds in the presence of orientifolds and D-branes. In examples, we find that the total topological string amplitude admits a BPS expansion only if the topological charge of the D-brane is equal to that of the orientifold plane. We interpret this as a manifestation of a general tadpole cancellation condition in the topological string that is necessary for decoupling of A- and B-model in loop amplitudes. Our calculations in the A-model...

Source: http://arxiv.org/abs/0712.2775v2

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47

Sep 18, 2013
09/13

by
Johannes Walcher

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Irrational invariants from D-brane superpotentials are pursued on the mirror quintic, systematically according to the degree of a representative curve. Lines are completely understood: the contribution from isolated lines vanishes. All other lines can be deformed holomorphically to the van Geemen lines, whose superpotential is determined via the associated inhomogeneous Picard-Fuchs equation. Substantial progress is made for conics: the families found by Mustata contain conics reducible to...

Source: http://arxiv.org/abs/1201.6427v1

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Sep 19, 2013
09/13

by
Daniel Krefl; Sara Pasquetti; Johannes Walcher

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We develop the real vertex formalism for the computation of the topological string partition function with D-branes and O-planes at the fixed point locus of an anti-holomorphic involution acting non-trivially on the toric diagram of any local toric Calabi-Yau manifold. Our results cover in particular the real vertex with non-trivial fixed leg. We give a careful derivation of the relevant ingredients using duality with Chern-Simons theory on orbifolds. We show that the real vertex can also be...

Source: http://arxiv.org/abs/0909.1324v2

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Sep 22, 2013
09/13

by
Oliver DeWolfe; Radu Roiban; Marcus Spradlin; Anastasia Volovich; Johannes Walcher

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The recent discovery of non-perturbatively stable two-dimensional string backgrounds and their dual matrix models allows the study of complete scattering matrices in string theory. In this note we adapt work of Moore, Plesser, and Ramgoolam on the bosonic string to compute the exact S-matrices of 0A and 0B string theory in two dimensions. Unitarity of the 0B theory requires the inclusion of massless soliton sectors carrying RR scalar charge as asymptotic states. We propose a regularization of...

Source: http://arxiv.org/abs/hep-th/0309148v1

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Sep 21, 2013
09/13

by
Radu Roiban; Christian Romelsberger; Johannes Walcher

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We investigate strings at singularities of G_2-holonomy manifolds which arise in Z_2 orbifolds of Calabi-Yau spaces times a circle. The singularities locally look like R^4/Z_2 fibered over a SLAG, and can globally be embedded in CICYs in weighted projective spaces. The local model depends on the choice of a discrete torsion in the fibration, and the global model on an anti-holomorphic involution of the Calabi-Yau hypersurface. We determine how these choices are related to each other by...

Source: http://arxiv.org/abs/hep-th/0203272v3

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Sep 23, 2013
09/13

by
David J. Gross; Johannes Walcher

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We use the \hat c=1 matrix model to compute the potential energy V(C) for (the zero mode of) the RR scalar in two-dimensional type 0B string theory. The potential is induced by turning on a background RR flux, which in the matrix model corresponds to unequal Fermi levels for the two types of fermions. Perturbatively, this leads to a linear runaway potential, but non-perturbative effects stabilize the potential, and we find the exact expression V(C)=\frac{1}{2\pi}\int da\arccos...

Source: http://arxiv.org/abs/hep-th/0312021v1

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Sep 17, 2013
09/13

by
Alex Buchel; Peter Langfelder; Johannes Walcher

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We study time-dependent solutions of Einstein-Maxwell gravity in four dimensions coupled to tachyon matter--the Dirac-Born-Infeld Lagrangian that provides an effective description of a decaying tachyon on an unstable D-brane in string theory. Asymptotically, the solutions are similar to the recently studied space-like brane solutions and carry S-brane charge. They do not break the Lorentzian R-symmetry. We study the tachyon matter as a probe in such a background and analyze its backreaction....

Source: http://arxiv.org/abs/hep-th/0207235v3

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49

Sep 21, 2013
09/13

by
Katrin Becker; Melanie Becker; Johannes Walcher

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We consider flux compactifications of type IIB string theory on the mirror of a rigid Calabi-Yau. In special cases, these models are dual to the type IIA flux vacua with runaway direction in flux space. We show that new weak coupling AdS solutions can be found for large complex structure, while Minkowski solutions with all moduli stabilized are confined to be at strong coupling. The existence of these solutions, as found in a previous work, is nevertheless guaranteed by a non-renormalization...

Source: http://arxiv.org/abs/0706.0514v1

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40

Sep 22, 2013
09/13

by
Kentaro Hori; Johannes Walcher

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B-type D-branes can be obtained from matrix factorizations of the Landau-Ginzburg superpotential. We here review this promising approach to learning about the spacetime superpotential of Calabi-Yau compactifications. We discuss the grading of the D-branes, and present applications in two examples: the two-dimensional torus, and the quintic.

Source: http://arxiv.org/abs/hep-th/0409204v1

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Sep 20, 2013
09/13

by
Amihay Hanany; Johannes Walcher

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Following the RG flow of an N=1 quiver gauge theory and applying Seiberg duality whenever necessary defines a duality cascade, that in simple cases has been understood holographically. It has been argued that in certain cases, the dualities will pile up at a certain energy scale called the duality wall, accompanied by a dramatic rise in the number of degrees of freedom. In string theory, this phenomenon is expected to occur for branes at a generic threefold singularity, for which the associated...

Source: http://arxiv.org/abs/hep-th/0301231v2

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Sep 18, 2013
09/13

by
Christopher P. Herzog; Johannes Walcher

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We discuss aspects of the dictionary between brane configurations in del Pezzo geometries and dibaryons in the dual superconformal quiver gauge theories. The basis of fractional branes defining the quiver theory at the singularity has a K-theoretic dual exceptional collection of bundles which can be used to read off the spectrum of dibaryons in the weakly curved dual geometry. Our prescription identifies the R-charge R and all baryonic U(1) charges Q_I with divisors in the del Pezzo surface...

Source: http://arxiv.org/abs/hep-th/0306298v3

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92

Jul 20, 2013
07/13

by
Simeon Hellerman; Johannes Walcher

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We resolve a puzzle in the theory of strings propagating on locally flat spacetimes with nontrivial Wilson lines for stringy Z_N gauge symmetries. We find that strings probing such backgrounds are described by consistent worldsheet CFTs. The level mismatch in the twisted sectors is compensated by adjusting the quantization of momentum of strings winding around the Wilson line direction in units of 1/(N^2 R) rather than 1/(N R), as might have been classically expected. We demonstrate in various...

Source: http://arxiv.org/abs/hep-th/0604191v1

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47

Sep 18, 2013
09/13

by
Katrin Becker; Melanie Becker; Cumrun Vafa; Johannes Walcher

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Type II orientifolds based on Landau-Ginzburg models are used to describe moduli stabilization for flux compactifications of type II theories from the world-sheet CFT point of view. We show that for certain types of type IIB orientifolds which have no Kahler moduli and are therefore intrinsically non-geometric, all moduli can be explicitly stabilized in terms of fluxes. The resulting four-dimensional theories can describe Minkowski as well as Anti-de-Sitter vacua. This construction provides the...

Source: http://arxiv.org/abs/hep-th/0611001v2

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65

Sep 21, 2013
09/13

by
Simeon Hellerman; Johannes Walcher

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We evaluate the problem of galaxy formation in the landscape approach to phenomenology of the axion sector. With other parameters of standard LambdaCDM cosmology held fixed, the density of cold dark matter is bounded below relative to the density of baryonic matter by the requirement that structure should form before the era of cosmological constant domination of the universe. Galaxies comparable to the Milky Way can only form if the ratio also satisfies an upper bound. The resulting constraint...

Source: http://arxiv.org/abs/hep-th/0508161v1

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Sep 20, 2013
09/13

by
Kentaro Hori; Kazuo Hosomichi; David C. Page; Raul Rabadan; Johannes Walcher

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After orientifold projection, the conifold singularity in hypermultiplet moduli space of Calabi-Yau compactifications cannot be avoided by geometric deformations. We study the non-perturbative fate of this singularity in a local model involving O6-planes and D6-branes wrapping the deformed conifold in Type IIA string theory. We classify possible A-type orientifolds of the deformed conifold and find that they cannot all be continued to the small resolution. When passing through the singularity...

Source: http://arxiv.org/abs/hep-th/0506234v2

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Sep 21, 2013
09/13

by
Andrew Neitzke; Johannes Walcher

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The open topological string partition function in the background of a D-brane on a Calabi-Yau threefold specifies a state in the Hilbert space associated with the quantization of the underlying special geometry. This statement is a consequence of the extended holomorphic anomaly equation after an appropriate shift of the closed string variables, and can be viewed as the expression of background independence for the open-closed topological string. We also clarify various other aspects of the...

Source: http://arxiv.org/abs/0709.2390v1

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44

Sep 22, 2013
09/13

by
Daniel Krefl; Johannes Walcher

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We study open string mirror symmetry for one-parameter Calabi-Yau hypersurfaces in weighted projective space. We identify mirror pairs of D-brane configurations, derive the corresponding inhomogeneous Picard-Fuchs equations, and solve for the domainwall tensions as analytic functions over moduli space. Our calculations exemplify several features that had not been seen in previous work on the quintic or local Calabi-Yau manifolds. We comment on the calculation of loop amplitudes.

Source: http://arxiv.org/abs/0805.0792v1

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Sep 18, 2013
09/13

by
Ilka Brunner; Kentaro Hori; Kazuo Hosomichi; Johannes Walcher

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We systematically construct and study Type II Orientifolds based on Gepner models which have N=1 supersymmetry in 3+1 dimensions. We classify the parity symmetries and construct the crosscap states. We write down the conditions that a configuration of rational branes must satisfy for consistency (tadpole cancellation and rank constraints) and spacetime supersymmetry. For certain cases, including Type IIB orientifolds of the quintic and a two parameter model, one can find all solutions in this...

Source: http://arxiv.org/abs/hep-th/0401137v1

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45

Sep 19, 2013
09/13

by
Daniel Krefl; Johannes Walcher

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We have recently shown that the global behavior of the partition function of N=2 gauge theory in the general Omega-background is captured by special geometry in the guise of the (extended) holomorphic anomaly equation. We here analyze the fate of our results under the shift of the mass parameters of the gauge theory. The preferred value of the shift, noted previously in other contexts, restores the Z_2 symmetry of the instanton partition function under inversion of the Omega-background, and...

Source: http://arxiv.org/abs/1010.2635v1

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Jul 20, 2013
07/13

by
Daniel Krefl; Johannes Walcher

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The partition function of an N=2 gauge theory in the Omega-background satisfies, for generic value of the parameter beta=-eps_1/eps_2, the, in general extended, but otherwise beta-independent, holomorphic anomaly equation of special geometry. Modularity together with the (beta-dependent) gap structure at the various singular loci in the moduli space completely fixes the holomorphic ambiguity, also when the extension is non-trivial. In some cases, the theory at the orbifold radius, corresponding...

Source: http://arxiv.org/abs/1007.0263v1

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55

Sep 20, 2013
09/13

by
Daniel Krefl; Johannes Walcher

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We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian...

Source: http://arxiv.org/abs/1207.1438v1

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53

Sep 24, 2013
09/13

by
Sebastian Franco; Yang-Hui He; Christopher Herzog; Johannes Walcher

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We briefly review our work on the cascading renormalization group flows for gauge theories on D-branes probing Calabi-Yau singularities. Such RG flows are sometimes chaotic and exhibit duality walls. We construct supergravity solutions dual to logarithmic flows for these theories. We make new observations about a surface of conformal theories and more complicated supergravity solutions.

Source: http://arxiv.org/abs/hep-th/0412207v2

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Sep 24, 2013
09/13

by
Johannes Walcher

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We evaluate the ideas of Pi-stability at the Landau-Ginzburg point in moduli space of compact Calabi-Yau manifolds, using matrix factorizations to B-model the topological D-brane category. The standard requirement of unitarity at the IR fixed point is argued to lead to a notion of "R-stability" for matrix factorizations of quasi-homogeneous LG potentials. The D0-brane on the quintic at the Landau-Ginzburg point is not obviously unstable. Aiming to relate R-stability to a moduli space...

Source: http://arxiv.org/abs/hep-th/0412274v4